1. Field of the Invention
The disclosed invention relates to active notch filters, and is particularly directed to a phase compensated active notch filter.
2. Background Art
Notch filters are typically utilized to remove a predetermined frequency or to remove a very small range of frequencies. As is well known, in physical realizations of a notch filter other frequencies on either side of the notch frequency will also be attenuated to varying degrees, such that the response characteristic of a notch filter resembles a notch.
While notch filters have been implemented as passive filters, active filter implementations have become popular as a result of advances in integrated circuit technology. Well-known active filter implementations include the state-variable implementations and the switched capacitor implementations of a second-order notch function. Examples of such implementations are set forth in the article "Improved Circuits for the Realization of Switched-Capacitor Filters," Martin, IEEE Transactions on Circuits and Systems, Vol. CAS-27, No. 4, April 1980, pp. 237-244.
Further examples of active biquadratic notch filters are set forth in U.S. Pat. No. 3,868,605, issued to Poole on Feb. 25, 1975; and in U.S. Pat. No. 4,242,642, issued to Laker et al. on Dec. 30, 1980.
Active filter implementation of a biquadratic notch filter typically includes two integrating stages wherein each stage includes an operational amplifier and an associated feedback capacitor. Two signal paths are provided between the input to the active filter and the input to the operational amplifier of the output integrating stage.
The primary signal path includes an input integrating stage and an output stage comprising a lossy integrator. If the input intergrating stage inverts the signal, then an inverting stage is interposed between the input integrating stage and the output integrating stage. The inverting stage may be realized with an operational amplifier or as part of a switched capacitor implementation of a resistive impedance. With ideal operational amplifiers, the feedback capacitor in the input integrating stage would result in 90 degrees of current lag in the primary signal path.
The secondary signal path typically includes a capacitor in parallel with the primary signal path for introducing 90 degrees of current lead. Ideally, at the notch frequency the current signals of the primary and secondary signal paths would be 180 degrees out-of-phase, and, assuming substantially equal amplitudes, would cancel to produce a current null at the input of the operational amplifier of the output integrating stage.
However, actual operational amplifiers are physical devices which do not behave ideally. Particularly, actual operational amplifiers introduce lagging phase shift, which creates an imbalance between the primary and secondary signal paths. As a result, the net current at the input to the output stage operational amplifier at the notch frequency is not zero and the depth of the notch is not infinite. Typically, the depth of the notch may be nominally about 40 db relative to the maximum signal. For some applications, that may be sufficient rejection, but other applications require greater rejection and therefore a deeper notch.